article · Physica Scripta
This research investigates the stochastic fractional Fokas system incorporating M-truncated derivatives. A specific wave transformation converts the governing equations into a one-dimensional conservative Hamiltonian system. Using the qualitative theory of dynamical systems, the bifurcation behaviour and phase portraits are analysed. Through the identification of conserved quantities, novel travelling wave solutions are derived for the system. Because the underlying Fokas system describes nonlinear pulse transmission within mono-mode optical fibres, these mathematical solutions provide a framework to study related physical phenomena. To demonstrate how the M-truncated derivative and the Wiener process alter system dynamics, the behaviours of the derived solutions are illustrated using two-dimensional and three-dimensional graphical representations.
Understanding how light pulses move through optical fibres is critical for maintaining signal integrity in communications technology. By modeling stochastic and fractional effects, this study provides mathematical solutions that capture realistic disturbances, aiding theoretical understanding of nonlinear optical phenomena.
This work represents early-stage theoretical research that could eventually inform the modeling and design of mono-mode optical fibre communications. Potential end users include optical engineers and telecommunications researchers studying nonlinear pulse transmission. However, the abstract demonstrates purely mathematical derivations and graphical simulations, indicating that practical application remains distant.
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Abstract In this study, the stochastic fractional Fokas system (SFFS) with M-truncated derivatives is considered. A certain wave transformation is applied to convert this system to a one-dimensional conservative Hamiltonian system. Based on the qualitative theory of dynamical systems, the bifurcation and phase portrait are examined. Utilizing the conserved quantity, we construct some new traveling wave solutions for the SFFS. Due to the fact that the Fokas system is used to explain nonlinear pulse transmission in mono-mode optical fibers, the given solutions may be applied to analyze an extensive variety of crucial physical phenomena. To clarify the effects of the M-truncated derivative and Wiener process, the dynamic behaviors of the various obtained solutions are depicted with 3-D and 2-D curves.
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DOI: 10.1088/1402-4896/ad30fd
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